Synchronization transitions caused by time-varying coupling functions. (English) Zbl 1462.34061
Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci. 377, No. 2160, Article ID 20190275, 16 p. (2019).
Summary: Interacting dynamical systems are widespread in nature. The influence that one such system exerts on another is described by a coupling function; and the coupling functions extracted from the time-series of interacting dynamical systems are often found to be time-varying. Although much effort has been devoted to the analysis of coupling functions, the influence of time-variability on the associated dynamics remains largely unexplored. Motivated especially by coupling functions in biology, including the cardiorespiratory and neural delta-alpha coupling functions, this paper offers a contribution to the understanding of effects due to time-varying interactions. Through both numerics and mathematically rigorous theoretical consideration, we show that for time-variable coupling functions with time-independent net coupling strength, transitions into and out of phase- synchronization can occur, even though the frozen coupling functions determine phase-synchronization solely by virtue of their net coupling strength. Thus the information about interactions provided by the shape of coupling functions plays a greater role in determining behaviour when these coupling functions are time-variable.
MSC:
| 34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |
| 34D06 | Synchronization of solutions to ordinary differential equations |
Keywords:
dynamical systems; coupling functions; coupled oscillators; interactions; applied mathematics; complexity; mathematical physicsReferences:
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